Reza H. Ahmadi

Batching and Scheduling Jobs on Batch and Discrete Processors

We consider a situation in which the manufacturing system is equipped with batch and discrete processors. Each batch processor can process a batch limited number of jobs simultaneously. Once the process begins, no job can be released from the batch processor until the entire batch is processed. In this paper, we analyze a class of two-machine batching and scheduling problems in which the batch processor plays an important role. Specifically, we consider two performance measures: the makespan and the sum of job completion times. We analyze the complexity of this class of problems, present polynomial procedures for some problems, propose a heuristic, and establish an upper bound on the worst case performance ratio of the heuristic for the NP-complete problem. In addition, we extend our analysis to the case of multiple families and to the case of three-machine batching.

Time-Cost Trade-Offs in Overlapped Product Development

Increasingly shorter product life cycles impel firms to design, develop, and market more products in less time than ever before. Overlapping of design and development stages is commonly regarded as the most promising strategy to reduce product development times. However, overlapping typically requires additional resources and can be costly.Our research addresses the trade-off between product development time and costs and introduces an algorithm to determine an appropriate overlapping strategy under different scenarios. The methodology developed was successfully employed at Rocketdyne Division of Rockwell International.

Concurrent Crashing and Overlapping in Product Development

This research addresses two common tools for reducing product development lead times: overlapping of development stages and crashing of development times. For the first time in the product development literature, a formal model addresses both tools concurrently, thus facilitating analysis of the interdependencies between overlapping and crashing. The results exhibit the necessity of addressing overlapping and crashing concurrently, and exhibit general characteristics of optimal overlapping/crashing policies. The impact of different evolution/sensitivity constellations on optimal policies is investigated, and comprehensive guidelines for structuring development processes are provided. For the special case of linear costs, an efficient procedure is presented that generates the efficient time-cost trade-off curves and determines the corresponding optimal overlapping/crashing policies. The impact of key parameters and the robustness regarding their estimates is illustrated with a simple two-stage example.

Structuring product development processes

Abstract This paper proposes operational frameworks for structuring product development processes. The primary objective of this research is to develop procedures to minimize iterations during the development process which adversely affect development time and costs. Several procedures are introduced to restructure the development process. The computation of the corresponding product development times is facilitated by two Markov models addressing different types of learning. The methodologies are employed to identify a set of managerial concerns in restructuring the product development processes. The developed framework has become an integral part of a re-engineering project for the development of rocket engines at Rocketdyne Division of Rockwell International. Throughout the paper, the methodologies are illustrated with the help of this process.

Managing Development Risk in Product Design Processes

Product development has become the focal point of industrial competition and is the cornerstone of long-term survival for most firms. One of the major management challenges in product development is to deal with development risk in the design process. In this paper we provide a strategic guideline as to how the design process should be managed and controlled. We describe how design reviews and engineering resources can be scheduled as the control mechanisms to operationally manage development risk. The methodologies developed are an integral part of a project to fundamentally restructure product design processes at Rocketdyne Division of Rockwell International, which designs and develops liquid-propellant rocket propulsion systems.

Component Fixture Positioning/Sequencing for Printed Circuit Board Assembly with Concurrent Operations

This paper considers the problem of positioning component fixtures on the carriers of computer, numerically controlled dual delivery machines used for populating printed circuit boards with surface mounted technology. This reel positioning problem RPP is one of a series of optimization problems that are critical for improving system productivity and realizing the full potential of concurrent operations. We formulate the RPP as a mathematical program and establish its complexity. Since the problem is NP-complete we focus on the development of heuristics. Our solution procedure was prompted by engineering considerations that included concerns for minimizing the changes in the carrier direction and total movement. We also present encouraging results with test problems. The method has been implemented and achieved 7 to 8% reductions in cycle time.

Managing Capacity and Flow at Theme Parks

The growth of service industries and their impact on the U.S. economy have attracted considerable attention in recent years. While some service sectors, most notably airline and telecommunication industries, have been in the forefront of model development, the industry is rather fragmented, and similar rigor is lacking in most other sectors. This paper describes an application of a model-based approach to some of the short-term ride capacity and visitor flow issues faced by the Six Flags Magic Mountain SFMM, a major national theme park. Specifically, we consider daily operations at the theme park and focus on the generation and evaluation of alternative strategies for managing ride capacities and visitor flow. Management of demand involves two aspects: a understanding customer preferences as revealed by routing behavior, and b using the model to evaluate the implications of changes in transition-behavior. A crucial component of the study relates to the empirical data collected. Besides verifying the validity of the models, these data provide several insights for developing schemes to manage the day-to-day operations of the park. The SFMM management was actively involved in various phases of this study and as a result has been introducing the proposed models in a phased manner.

Routing heuristics for automated pick and place machines

We examine the problem of sequencing the placements of multiple part types for a computer controlled placement machine. The problem is modeled as a collection of interdependent traveling salesman problems. A heuristic based on a space filling curve is shown to be easy to compute and quite effective. Numerical experiments show that on problems of realistic size our heuristics show very little divergence from optimality. The probabilistic analysis of the proposed heuristic indicates that the proposed heuristics are asymptotically optimal. Finally we use our heuristic to perform the sequencing operation on real placement machines. The results of this experiment are in accord with our numerical simulations. The main ideas of this study have become part of the control system currently in use in a large electronic card assembly facility that produces approximately 12,000 boards per day. Improvements in throughput of between 4% and 9% have been reported.

The line segmentation problem

This paper describes a line segmentation problem in a multistage, multimachine production system. The production facility can concurrently produce several types of circuit boards because each production stage consists of multiple machines. The items produced are categorized into families, and items belonging to the same family share the common major setup, while switching over from one family to another requires a major setup. The line segmentation problem determines an allocation of machines at each production stage to families so as to minimize the time to complete all jobs. As a result of segmenting the line, several minilines are formed which are dedicated to the production of items in each family. Forming dedicated minilines and producing the items in a family on the same line captures the benefits of group technology and focused factory. We first formalize the line segmentation problem as a quadratic integer programming problem, and establish its NP-completeness. Since the problem is NP-complete, we...

Lower bounds for single-machine scheduling problems

This article addresses deterministic, nonpreemptive scheduling of n jobs with unequal release times on a single machine to minimize the sum of job completion times. This problem is known to be NP-hard. The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.